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Register a new userEffect of Thermal Conductivity, Compressive Viscosity and Radiative Cooling on the Phase Shift of Propagating Slow Waves with and without Heating-Cooling Imbalance
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A.K. Srivastava Dr.
Publication date
2021
fields
Physics
and research's language is
English
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We study phase shifts of the propagating slow waves in coronal loops invoking the effects of thermal conductivity, compressive viscosity, radiative losses and heating-cooling imbalance. We derive a general dispersion relation and solve it to determine phase shifts of density and temperature perturbations relative to the velocity and their dependence on equilibrium parameters ($rho_0$, $T_0$). We estimate phase difference ($Delta phi$) between density and temperature perturbations and its dependence on $rho_0$ and $T_0$. The effect of viscosity on the phase shifts was found negligible. The role of radiative losses along with h/c imbalance for chosen specific heating function ($H(rho, T) propto rho^{-0.5} T^{-3}$) in determining phase shifts, is found to be significant for the high density and low temperature loops. The h/c imbalance can increase the phase difference ($Delta phi approx 140^circ$) for low temperature loops compared to the constant heating case ($Delta phi approx 30^circ$). We derive a general expression for the polytropic index. We find that in the presence of thermal conduction alone, the polytropic index remains close to its classical value for all the considered $rho_0$ and $T_0$. However, it reduces to a value $1.2$ when loop density is decreased by an order of magnitude compared to its normal coronal value. We find that the inclusion of radiative losses, with or without h/c imbalance, cannot explain the observed polytropic index. The thermal ratio ($d$) needs to be enhanced by an order of magnitude, in order to explain its observed value $1.1 pm 0.02$ in the solar loops. We also explore the role of different heating functions for typical coronal parameters and found that although the polytropic index remains close to its classical value, the phase difference is highly dependent on the form of heating function (The abstract is restructured for arxiv).
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Acoustic and magnetoacoustic waves are among the possible candidate mechanisms that heat the upper layers of solar atmosphere. A weak chromospheric plage near a large solar pore NOAA 11005 was observed on October 15, 2008 in the lines Fe I 617.3 nm and Ca II 853.2 nm with the Interferometric Bidimemsional Spectrometer (IBIS) attached to the Dunn Solar Telescope. Analyzing the Ca II observations with spatial and temporal resolutions of 0.4 and 52 s, the energy deposited by acoustic waves is compared with that released by radiative losses. The deposited acoustic flux is estimated from power spectra of Doppler oscillations measured in the Ca II line core. The radiative losses are calculated using a grid of seven 1D hydrostatic semi-empirical model atmospheres. The comparison shows that the spatial correlation of maps of radiative losses and acoustic flux is 72 %. In quiet chromosphere, the contribution of acoustic energy flux to radiative losses is small, only of about 15 %. In active areas with photospheric magnetic field strength between 300 G and 1300 G and inclination of 20-60 degrees, the contribution increases from 23 % (chromospheric network) to 54 % (a plage). However, these values have to be considered as lower limits and it might be possible that the acoustic energy flux is the main contributor to the heating of bright chromospheric network and plages.
The processes of the coronal plasma heating and cooling were previously shown to significantly affect the dynamics of slow magnetoacoustic (MA) waves, causing amplification or attenuation, and also dispersion. However, the entropy mode is also excited in such a thermodynamically active plasma and is affected by the heating/cooling misbalance too. This mode is usually associated with the phenomenon of coronal rain and formation of prominences. Unlike the adiabatic plasmas, the properties and evolution of slow MA and entropy waves in continuously heated and cooling plasmas get mixed. Different regimes of the misbalance lead to a variety of scenarios for the initial perturbation to evolve. In order to describe properties and evolution of slow MA and entropy waves in various regimes of the misbalance, we obtained an exact analytical solution of the linear evolutionary equation. Using the characteristic timescales and the obtained exact solution, we identified regimes with qualitatively different behaviour of slow MA and entropy modes. For some of those regimes, the spatio-temporal evolution of the initial Gaussian pulse is shown. In particular, it is shown that slow MA modes may have a range of non-propagating harmonics. In this regime, perturbations caused by slow MA and entropy modes in a low-$beta$ plasma would look identically in observations, as non-propagating disturbances of the plasma density (and temperature) either growing or decaying with time. We also showed that the partition of the initial energy between slow MA and entropy modes depends on the properties of the heating and cooling processes involved. The obtained exact analytical solution could be further applied to the interpretation of observations and results of numerical modelling of slow MA waves in the corona and the formation and evolution of coronal rain.
The crisis of the standard cooling flow model brought about by Chandra and XMM-Newton observations of galaxy clusters, has led to the development of several models which explore different heating processes in order to assess if they can quench the cooling flow. Among the most appealing mechanisms are thermal conduction and heating through buoyant gas deposited in the ICM by AGNs. We combine Virgo/M87 observations of three satellites (Chandra, XMM-Newton and Beppo-SAX) to inspect the dynamics of the ICM in the center of the cluster. Using the spectral deprojection technique, we derive the physical quantities describing the ICM and determine the extra-heating needed to balance the cooling flow assuming that thermal conduction operates at a fixed fraction of the Spitzer value. We assume that the extra-heating is due to buoyant gas and we fit the data using the model developed by Ruszkowski and Begelman (2002). We derive a scale radius for the model of $sim 5$ kpc, which is comparable with the M87 AGN jet extension, and a required luminosity of the AGN of a $few times 10^{42}$ erg s$^{-1}$, which is comparable to the observed AGN luminosity. We discuss a scenario where the buoyant bubbles are filled of relativistic particles and magnetic field responsible for the radio emission in M87. The AGN is supposed to be intermittent and to inject populations of buoyant bubbles through a succession of outbursts. We also study the X-ray cool component detected in the radio lobes and suggest that it is structured in blobs which are tied to the radio buoyant bubbles.
Context. The radiative energy balance in the solar chromosphere is dominated by strong spectral lines that are formed out of LTE. It is computationally prohibitive to solve the full equations of radiative transfer and statistical equilibrium in 3D time dependent MHD simulations. Aims. To find simple recipes to compute the radiative energy balance in the dominant lines under solar chromospheric conditions. Methods. We use detailed calculations in time-dependent and 2D MHD snapshots to derive empirical formulae for the radiative cooling and heating. Results. The radiative cooling in neutral hydrogen lines and the Lyman continuum, the H and K and intrared triplet lines of singly ionized calcium and the h and k lines of singly ionized magnesium can be written as a product of an optically thin emission (dependent on temperature), an escape probability (dependent on column mass) and an ionization fraction (dependent on temperature). In the cool pockets of the chromosphere the same transitions contribute to the heating of the gas and similar formulae can be derived for these processes. We finally derive a simple recipe for the radiative heating of the chromosphere from incoming coronal radiation. We compare our recipes with the detailed results and comment on the accuracy and applicability of the recipes.
Acoustic and magnetoacoustic waves are considered to be possible agents of chromospheric heating. We present a comparison of deposited acoustic energy flux with total integrated radiative losses in the middle chromosphere of the quiet Sun and a weak plage. The comparison is based on a consistent set of high-resolution observations acquired by the IBIS instrument in the Ca II 854.2 nm line. The deposited acoustic-flux energy is derived from Doppler velocities observed in the line core and a set of 1737 non-LTE 1D hydrostatic semi-empirical models, which also provide the radiative losses. The models are obtained by scaling the temperature and column mass of five initial models VAL B-F to get the best fit of synthetic to observed profiles. We find that the deposited acoustic-flux energy in the quiet-Sun chromosphere balances 30-50 % of the energy released by radiation. In the plage, it contributes by 50-60 % in locations with vertical magnetic field and 70-90 % in regions where the magnetic field is inclined more than 50 degrees to the solar surface normal.
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